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Adaptive Speckle Imaging Interferometry: a
new technique for the analysis of microstructure dynamics, drying processes and
coating formation.
L. Brunel1*, A. Brun1, P. Snabre2 , L. Cipelletti3
(1) FORMULACTION, 10 Impasse Borde Basse, F-31240 L’Union , France.
http://www.formulaction.com
(2) CRPP, CNRS, avenue Albert Schweitzer, F-33600 Pessac, France
(3) LCVN and Institut Universitaire de France, CNRS UMR 5587, Université Montpellier II, Pl.
E. Bataillon 34095 Montpellier Cedex 05, France
*Corresponding author: [email protected]
Abstract: We describe an extension of multi-speckle diffusing wave
spectroscopy adapted to follow the non-stationary microscopic
dynamics in drying films and coatings in a very reactive way and with
a high dynamic range. We call this technique “Adaptive Speckle
Imaging Interferometry”. We introduce an efficient tool, the interimage distance, to evaluate the speckle dynamics, and the concept of
“speckle rate” (SR, in Hz) to quantify this dynamics. The adaptive
algorithm plots a simple kinetics, the time evolution of the SR,
providing a non-invasive characterization of drying phenomena. A
new commercial instrument, called HORUS®, based on ASII and
specialized in the analysis of film formation and drying processes is
presented.
© 2007 Optical Society of America
OCIS codes: (030.6600) Statistical optics; (030.6140) Speckle; (120.6160) Speckle
interferometry; (290.0290) Scattering; (290.4210) Multiple scattering; (290.5850)
Scattering, particles
References
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20. A look up table can be also used for the multiplication, but its size would be the square of the size of
the one used for computing the square. For 8-bit numbers, the LUT used for the square has 256 entries
while the one used for the multiplication has 65536 entries.
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23. L/l* is estimated by comparing measurements of the backscattered flux to results from Monte Carlo
simulations of the photon propagation in a random scattering medium, where L/l* is tuned to reproduce
the experimental measurements.
1. Introduction
Besides direct observation using a microscope, the first known optical technique to
analyze the dynamical behavior of micrometric particle suspensions is Dynamic
Light Scattering (DLS) [1,2], sometime also referred to as Photon Correlation
Spectroscopy (PCS). The optical set-up consists in a point-like detector, usually a
phototube or an avalanche photodiode, which collects the light scattered by the
particles at a fixed angle with respect to the propagation direction of the incident
light, usually a coherent laser beam. As the particles move (e.g. because of Brownian
motion), the relative phase of the scattered photons change, resulting in temporal
fluctuations of the detected intensity. These fluctuations are characterized by
measuring their time auto-correlation function g2()=<I(t)I(t+)>time/<I2>time, with I(t)
the time-dependent scattered intensity and  the time delay. For Brownian particles
under single scattering conditions, g2 decays exponentially with a decay time that
depends on the particles’ diffusing coefficient [2], thus providing a popular particle
sizing method. In 1987, Maret and Wolf [3] proposed an analytic formula for g2 for
Brownian scatterers in the opposite limit of strong multiple scattering, where photons
undergo a large number of scattering events along their path through the sample. In
1988, Pine et al. [4] introduced the expression “Diffusing Wave Spectroscopy”
(DWS) to designate DLS under strong multiple scattering conditions; since then,
DWS has become a powerful and widespread technique for characterizing colloidal
suspensions [5].
In traditional DLS and DWS techniques, achieving a good signal/noise ratio
requires g2 to be averaged over at least 1000 times its characteristic decay time. For
samples with a slow dynamics (e.g. concentrated or aggregating suspensions) this
may require a too long measurement time. Moreover, for non-stationary dynamics
(e.g. in aggregation or drying processes) extensive time averaging may lead to
incorrect results, if the dynamics evolves significantly during the measurement time.
Recently, these limitations have been circumvented by sampling a large number of
speckles. To fix the ideas, let us consider the case of a DWS experiment with a single
point-like detector. As recalled above, about 1000 statistically independent samples
are needed to build a good correlation function. These samples are usually collected
sequentially in time, assuming that time averaging is equivalent to averaging in the
ensemble of photon paths. This condition is normally met, since the scatterers move
substantially and explore a significant fraction of all possible configurations during
the measurement time. Thus time and ensemble averages are equivalent, a condition
referred to as ergodicity. In other words, if the sample micro-structure evolves
rapidly enough, a sufficiently large fraction of all possible light paths may be
sampled in a reasonable time and time averaging yields the desired ensemble
average.
For slow or non-stationary dynamics, various schemes have been proposed to
speed-up this sampling process, in addition to introducing methods to correct for
insufficient time-averaging [6]. In the cell-scanning technique [7] and the two cells
technique [8] (or its rotating-frosty-glass variant [9]) a point-like detector is
illuminated sequentially by different speckles, either by scanning the beam through
the sample or by “scrambling” the scattered photons by letting them go through an
additional scatterer before being detected (the 2 nd cell or the rotating frosty glass). In
the so-called “multispeckle” methods [9,14-17], by contrast, different speckles are
sampled in parallel by using a large number of independent detectors, usually the
pixels of a Charge Coupled Device (CCD) or CMOS camera (it is also possible to use
a series of single photo-diodes or optical fibers coupled to photo-diodes). A
correlation function is computed for each pixel, and the desired ensemble-averaged
g2 is obtained by averaging over all pixels: g2()=<I(t)I(t+)>pixels/<I2>pixels. By
adjusting the detection optics in such a way that the speckle size matches the pixel
size (typically of the order of 10 µm), one ensures that each pixel carries a
statistically independent contribution to g2 and that the overall signal/noise ratio is
maximized [9]. The acquisition time required to achieve a given precision, compared
to that with a single detector, is reduced by a factor equal to the number of pixels.
Since the latter is typically as large as several tens of thousands, in practice no time
averaging at all is required, thus providing access to the instantaneous dynamics.
Together with the capability of measuring slow and non-stationary dynamics,
advantages include a simpler set-up and a cost per detector (pixel) very low. The
limitations are the reduced speed and sensitivity of CCD and CMOS cameras
compared to avalanche photo-diodes or phototubes. The maximum acquisition rate is
30Hz for a classical cheap camera and about a few kHz for more sophisticated and
expensive cameras, limiting the smallest accessible delay to a fraction of msec at
best, instead of about 10 nsec for traditional point-like detectors.
In this work we present three new developments of the multi-speckle technique.
First, we propose a new tool to quantify the evolution of the speckle pattern recorded
by a CCD or CMOS camera, which we term the inter-image distance. Second, we
show that for most cases of practical importance in film formation and drying
processes, the inter-image distance grows with time and saturates according to a
simple exponential law. This allows us to introduce an efficient and quick way to
quantify the rate of change of the speckle pattern which we term Speckle Rate, (SR).
Third, we present an adaptive algorithm that continuously adjusts the camera
acquisition rate to trace in real time the speckle dynamics with high reactivity,
dynamic range and accuracy. We globally term “Adaptive Speckle Imaging
Interferometry” (ASII) these three advances. ASII is thus an extension of multispeckle (MS) DWS adapted to characterize film formation and drying processes by
plotting a simple kinetics, the time evolution of the SR, providing a new, noninvasive signature of micro-structure evolution.
As a final introductory remark, we note that the temporal evolution of the speckle
pattern generated by a sample with internal dynamics has also been investigated as a
natural extension of the early works on the statistics of frozen speckles, often in
connection with metrology and holography studies [10]. The scientific community
involved in these works (oddly somehow separated from the DLS and DWS ones)
refers to this phenomenon as to “dynamic speckle”. The most popular way to
characterize the “dynamic speckle” phenomenon is to measure the contrast < I2 >/< I
>2 of the speckle pattern, the underlying idea being that fast-moving speckles would
lead to a blurred speckle pattern and hence to a reduced contrast. Both point-like [10]
and CCD detectors [11] has been used in measurements over a variety of samples,
ranging from biological tissues [10] to paint films [11] similar to those explored in
our work. Compared to our approach, speckle contrast techniques yield less
information, since the dynamics is probed on a single time scale, the integration time
over which the detector is exposed to the speckle pattern. By contrast, in our
technique the inter-image distance is calculated for time lags  spanning several
decades. As we shall show in the following, this is a crucial requirement for
characterizing the dynamics of film, since the speckle rate may vary over 4 orders of
magnitude.
More sophisticated approaches, involving the calculation of correlation functions
similar to g2 or to the inter-image distance introduced here have been used to
characterize the drying of coatings in Refs. [12] and [13], respectively. In [12], a
point-like detector was used, thus requiring a temporal average of the correlation
function. This limits the effectiveness of this technique when the dynamics are very
slow and non-stationary, as discussed above for DLS and DWS. In [13], a CCD
detector was used. The second order moment, IM, of the so-called modified cooccurrence matrix was calculated, a quantity similar to the inter-image distance
defined here. However, IM was calculated for a single fixed time delay, whereas in
our work the inter-image distance is calculated for several ‘s and the minimum lag is
continuously optimized by varying the CCD acquisition rate. This allows us to
characterize the film dynamics with great accuracy and in real time over more than
four orders of magnitude in time, an achievement not possible with the method
proposed in [13].
This short overview of previous works in the field of DLS and DWS and in that,
closely related, of dynamic speckle interferometry shows that the ASII method
proposed here represents a significant advance with respect to the existing optical
techniques for the characterization of film formation and drying. The ASII method is
at the core of a new commercially available instrument called HORUS®, which
monitors the drying process of any product deposited on any substrate by analyzing
the micro-structure dynamics of the film [18]. HORUS® provides the ink and paint
industries with a new valuable tool for the non-intrusive monitoring of the drying and
film formation process.
The paper is organized as follows: the hardware configuration is described in
Section 2. Section 3 explains the ASII method: the inter-image distance, the
exponential approximation and the adaptive algorithm are described here. Some
examples of the application of HORUS® to the analysis of film formation are given
in Section 4, before the concluding remarks of Section 5.
2. Horus® hardware configuration
A backscattering configuration has been chosen for the HORUS® apparatus,
allowing the detector and the laser source to be housed in a single convenient optical
head, as shown in Fig. 1. Typically, the backscattered signal is higher than the
transmitted one, allowing one to use a detector with a relatively low sensitivity (such
as a CCD or a CMOS camera) and limiting the required laser power. This last point is
important for safety reasons and for preventing heat-induced convection in the
sample. Indeed, in the backscattering geometry even a low-power laser diode allows
one to monitor the drying of relatively black products such as black paints or inks.
The product to be studied is spread out in a thin layer on any chosen substrate.
Mechanical stability is important, since any vibration of the optical head would result
in a spurious loss of correlation, wrongly attributed to the micro-structure dynamics
of the analyzed product. The substrate is thus fixed on a massive support plate, which
is carefully leveled with respect to gravity in order to avoid any flow. The optical
head is attached to a rigid vertical mast fixed to the plate. The apparatus is designed
so as to filter out any external vibration, limiting the maximum displacement of the
head with respect to the plate to less than 1 m. The head contains a CMOS camera
detector (with no lens) and the laser source. A hole acting as a diaphragm blocks the
parasitic ambient light coming from outside a cone of half-angle approximately 10
degrees. To remove the remaining parasitic light propagating within this cone, an
interference filter of bandwidth 10 nm is placed in front of the hole. The laser source
is a standard and safe laser diode with power 0.9 mW and wavelength 650 nm. An
adjustable focusing lens is mounted in front of the laser to adjust the spot size on the
product, typically to a few mm.
The camera has a 320x240 pixel sensor with a maximum frame rate of 30
images/s. The slowest micro-structure movement detectable by HORUS® is
ultimately limited by mechanical stability. The minimum measurable speckle rate is
around 10-5 Hz, corresponding to a correlation time c of 100000 seconds, slightly
more than 1 day. The maximum accessible speckle rate is limited by the camera
speed itself. As explained below, the algorithm imposes the capture of a minimum of
4 images in order to calculate the SR: the maximum SR is thus limited to about
10Hz.
Fig. 1. The HORUS® setup.
3. The ASII method: inter-image distance, exponential approximation and
adaptive algorithm
3.1 Inter-image distance
In order to minimize the computation load needed to monitor the drying process, one
may wonder whether the evolution of the speckle pattern may be characterized more
efficiently than by calculating the intensity correlation function g 2. A convenient way
to address this question is to think at a speckle image as a point in a multidimensional space Sim. For any given image, each co-ordinate in the hyper-space Sim
corresponds to the intensity measured at a given pixel of the CMOS camera. The
dimensionality of Sim is thus the number of pixels of the camera, n=76800 for our
320x240 camera. The change of the speckle pattern between two images may then be
quantified by introducing a vectorial distance function between the corresponding 2
points in the space Sim.
electronic images ----> space Sim
(image1,image2) |----> (p1,p2) in Sim
------> R+
|-----> distance
The distance is by definition a single non-negative number, which can be used to
compare quantitatively pairs of speckle images taken at different times. If the two
images are identical, the corresponding points in the hyper-space Sim coincide and
their distance is zero. As the two images become different, their distance will
increase.
Various definitions for the distance function may be chosen; here we discuss
briefly two possible choices that are computationally appealing. Let's note I 1(x,y) the
intensity of a pixel of co-ordinates (x,y) of the first image and I2(x,y) the
corresponding intensity for the second image. We define a quadratic vectorial
distance d2={[I2(x,y)-I1(x,y)]2}1/2, as well as an alternative distance d1=|I2(x,y)I1(x,y)|. In both cases, the sum is over all pixels. The inter-image distance has an
asymptotic maximum value that we shall call d max, corresponding to two fully
uncorrelated speckle images. As we show below, both d 1 and d2 are less demanding
in terms of computational power than the traditional correlation function g2. In the
HORUS® apparatus we have chosen to implement d2, which, as we will discuss
below, is directly related to the more common g2 function. Note that this quadratic
inter-image distance represents the extension to multi-speckle processing of the
“structure function” introduced by Schätzel for point-like detectors, which was
shown to be less prone to detector noise than g2 [19].
3.2 Comparison of the computational load
For the case of an ideal, noise-free detector with n pixels, computing g2 requires n
multiplications, while d2 needs n differences and n squares, and d1 needs n
differences and n absolute values. Computing an addition is faster than a
multiplication and easier to implement in a specialized electronics. Taking a square
can be at least as fast as an addition thanks to a (small) look-up table [20]. Thus, the
intensity correlation function g2 is the most time consuming and the inter-image
difference d1 the less time consuming way to quantify the speckle pattern evolution.
The inter-image distance has also some additional advantages in the case of nonideal detectors. A first typical imperfection is the fact that each pixel has its
individual offset, or dark level. This offset must be corrected for when calculating g2
[16], requiring two more additions per pixel, while it is automatically removed when
using d2 or d1. Table 1 below recapitulates the computational cost of the various
schemes discussed above, for the case of a camera having pixels with distinct offsets:
Table 1. Computational cost of various correlation tools, including camera offset calibration
tool additions or subtractions
squares
multiplications
Needs offset calibration
tool additions or subtractions
squares
multiplications
Needs offset calibration
g2
2n
0
n
yes
d2
n
n
0
no
d1
n
0
0
no
It appears clearly that the distances d1 or d2 allow for a signal processing faster
than that required for the traditional intensity auto-correlation.
Note that it is possible to establish a relation between d2 and g2 involving only on
the mean intensity, < I >, and the mean squared intensity, < I2 >. By assuming that the
probability distribution of the scattered intensity is the same for each pixel and using
the classical relation between the variance and covariance of two random variables,
one finds:
d2=[2n(< I2 >-g2< I >2)]1/2
(1)
In particular, the maximum inter-image distance corresponding to two completely
uncorrelated images (for which g2-1= 0) can be calculated using the previous relation,
yielding d2max=[2n(< I2 >-< I >2)]1/2. Therefore, d2max may be calculated directly from
the probability distribution function (PDF) of the intensity obtained from one single
speckle image, provided that the dark level offset is the same for all pixels.
If the speckle size is much larger than the pixel size, the PDF P(I) of the scattered
intensity is exponential: P(I)=(1/< I >)exp(-I/< I >) [21]. In this case < I2 >=2< I >2
and the relationship between g2 and d2 simplifies to g2-1=1-(d2/d2max)2, with
d2max=(2n)1/2 < I >.
3.3 Estimation of the characteristic rate of change of the speckle field by an
exponential approximation.
In order to monitor a drying process, a series of short movies of the speckle pattern
backscattered by the sample is acquired. Each movie is processed independently to
extract the information related to the speckle dynamics. For each movie, the interimage distance, d2(), between the first image of the movie and all subsequent
images, is calculated. Typical examples for three different drying fluids are shown in
Fig. 2. For the sake of simplicity, it is desirable to extract only one single figure
representative of the speckle dynamics for each movie. Experimentally, we have
noticed that the shape of d2() is very often well described by an exponential growth
to d2max, the saturation level:
d2()=d20+(d2max-d20)[1-exp(/c)]
0
(2)
0
with d2 the d2 value for the first pair of images. Note that d2 may be significantly
larger than zero due to electronic noise and speckle dynamics faster than the
minimum lag between images. It is therefore natural to fit the data to Eq. (2) and take
the characteristic time c for the typical decay time we are looking for. Finally, we
define the “speckle rate” (SR) as the inverse of the correlation time c, SR=1/c, in
order to provide a single number that decreases as the dynamics slows down.
Two practical issues are worth discussing. First, the asymptotic value of d2 (d2max)
is required in Eq. (2). As discussed above, d2max could be calculated from the PDF of
the speckle intensity for one single image. However, we find that more robust results
are obtained by evaluating d2max using a pair of fully decorrelated speckle images,
which we obtain from the first image and a software-rotated version of it. Second, we
aim to extract the SR as rapidly as possible, in order to follow the drying kinetics.
Once d2max is known, this may be achieved by acquiring a shorter speckle movie,
covering only the initial, linear growth of d2. c is then obtained by intersecting the
initial linear growth with the asymptote d2max. Practically, a linear adjustment of the
d2 data is performed and extrapolated until the horizontal line d2 = d2max is crossed.
This fitting procedure filters out most of the measurement noise. We have found that
acquiring speckle images during c/4 yields satisfactory results. Therefore, the SR can
be measured in a quarter of the speckle field characteristic time.
3.4 Adaptive algorithm
Ideally, each movie has a duration T=c/4 and contains as much images as possible.
Since the dynamics is usually non-stationary, the value of T must be permanently
adapted before acquiring the next movie. We start by an initial guess T1 = 100 ms,
and calculate the first value of the SR, SR1, as explained above. SR1 is used as an
input to calculate the duration of the following movie, which is set to T2 = 1/(4SR1).
This procedure is iterated during the whole measurement. Once the duration Ti of the
i-th has been set, the frame rate for the i-th movie is chosen as large as possible,
within the limits of the camera (30 Hz) and with the additional constraint that each
movie contains at most 255 images (for computational efficiency).
This algorithm acts as an efficient feed-back loop: if the first guess is not correct,
the algorithm converges rapidly towards the correct one. If c evolves during the
drying process, the algorithm will adapt the acquisition and processing to the new
one. Even if c drops abruptly (e.g. if the speckle field “freezes” rapidly), the reduced
time needed to evaluate the SR ( c/4) allows a fast convergence to be achieved.
4. Experimental tests
4.1 Examples of inter-image distance curves
Figure 2 shows three typical examples of normalized inter-image distance curves,
together with fits according to Eq. (2) . The first curve to the left (c= 1s) was
recorded during the drying of a white correction fluid. The intermediate one (c= 5s)
is from an acrylic white paint, while the slowest drying process (right curve, c= 9 s)
was measured during the drying of a red marker pen ink on metal. Note that in all
cases the data are in excellent agreement with the exponentially saturating growth,
Eq. (2).
Fig 2. Normalized inter-image distance d2/dmax versus time for white
corrector (blue line), acrylic paint (red line) and marker pen ink (green line).
The black lines are fits according to Eq. (2).
4.2 Examples of speckle rate kinetics curve
We present in Fig. 3 three examples of drying experiments performed with
HORUS®. The first two examples concern the film formation of a paint layer of 40
µm of thickness. The first one is an organic-solvent-based paint applied on a glass
substrate (blue curve in Fig. 3). The SR vs time curve exhibits a first plateau at 2000
s, which corresponds to the end of volatile solvent evaporation, or “dry-to-touch”
time in the paint industry language. The speckle rate reaches a final plateau at 10 -4 Hz
after 22000 s, when the paint is “dry-hard”. The orange curve in Fig. 3 shows the
drying process of a water-based latex paint applied to a metal substrate. Note the
large fluctuations of the speckle rate around 200 s, likely due to the packing process
of the colloidal particles contained in the paint during the film formation. This
temporally heterogeneous dynamics is strongly reminiscent of that of jammed
colloids [22]. The “dry-to-touch” plateau is reached at 800 s and the “dry-hard”
plateau is reached after 5000 s. The third experiment shown in Fig. 3 (red curve) is
the drying of a mark left by a commercial pen marker on a glassed paper.
Collectively, the data shown in Fig. 3 illustrate the capability of HORUS® to follow
both very slow or rapid drying processes and to capture even quite abrupt changes in
the speckle rate evolution, as, e.g., the sharp drop of the SR around t = 10 s for the
pen marker ink.
Fig. 3. Rate of change of the speckle pattern, SR, versus time in a double
logarithmic graph. The fastest-drying curve (left, red) is for a commercial marker
pen, the middle one is for a water-based paint (middle, orange) and the longest
drying curve if for a organic solvent- based paint (right, blue).
4.3 Penetration depth
One question of practical importance is how deep in a drying film HORUS® can
detect some motion: in other words, can this apparatus monitor the drying of the
material below a superficial layer where a solid skin has been already formed. To
address this issue, a simple experiment has been performed. A layer of perfectly dry
paint with a known thickness and photon transport mean free path l* [4] is placed on
a transparent glass substrate. Another layer of fresh paint is spread below the glass
plate. The purpose of the experiment is to determine the maximum thickness, L, of
dry paint beyond which HORUS® does not detect anymore the dynamics in the fresh
paint. We find that L depends almost only on the photon transport mean free path l*
of the dry paint, especially in the limit L>>l*. In particular, for L/l* > 30 [23] the
fresh layer is not detected anymore, indicating that its contribution to the inter-image
distance becomes smaller than the measurement noise. The penetration depth L is
then at least 30 l*, which corresponds to 150 m to 600 m for a classical white paint
(the l* value for a paint goes from 5 to more than 20 m).
4.4 Influence of concentration, thickness and support
In order to check the impact on the measurement of the film thickness and of the
particle content, we have prepared two suspensions of Titanium dioxyde particles in
castor oil (viscosity: 1 Pa.s at 21 °C): one with a volume fraction =1 % (l*=300
m) and one with =0.1 % (l*=3000 m). Note that since the boiling point of castor
oil is around 300 ºC, the product is not drying at all during the experiment: the
speckle rate SR is thus stationary. To avoid border effects, a large stripe of width 5
cm is spread on the substrate using a special tool. For the first suspension (=1 %)
spread on a metallic substrate, a layer of thickness 1000 m gives a speckle rate of 7
Hz, 250 m gives 3.2 Hz and 80 m gives 1.5 Hz. For the second suspension (=0.1
%) also spread on a metallic substrate, the layer of thickness 1000 m gives a speckle
rate of 0.5 Hz, 250 m gives 0.4 Hz and 80 m gives 0.02 Hz. Therefore, decreasing
the layer thickness or particle volume fraction reduces the mean number of photon
scattering events in the film [5] and hence decreases the speckle rate. This example
shows that it is mandatory to control carefully the layer thickness when comparing
absolute SR’s measured for different products.
To check the effect of the substrate color or albedo on the measured SR, we have
performed measurements for two different substrates: the black and the white part of
a standard paper test chart used in paint industry. The albedo for the wavelength used
is almost one for the white part and 0.125 for the black substrate. For the black
substrate, the majority of the photons reaching the substrate are absorbed. By
contrast, part of the photons reaching the white substrate diffuse in the (static)
structure of the substrate and eventually are backscattered through the paint to the
detector. The drying process of a layer of thickness 5 m of a white acrylic paint (l*
about 15 m and L/l*=5) is measured for both substrates. Monte Carlo simulations
show that the mean number of backscattered photons is about 3 times higher for the
white substrate than for the black one. As a consequence, one expects a speckle rate
about 3 times lower for the black substrate than for the white one. Indeed, the SR
kinetics measured for the two substrates have the same shape, but the one
corresponding to the black substrate is lower by a factor of about 3 with respect to
that obtained for the white substrate, as shown in Fig. 4. Therefore, the substrate
color or albedo does not affect the shape of the drying curve, an important feature in
industrial applications.
Fig. 4. Rate of change of the speckle pattern, SR, versus time in a semi
logarithmic graph, for the drying of a 75m layer of an acrylic paint. The
blue curve (higher SR) corresponds to a white substrate and the red curve
(lower SR) corresponds to a black substrate. There is a ratio of
approximately 3 between the absolute magnitudes of the 2 curves, but the
shape of SR vs t is insensitive to the substrate color.
5. Conclusion
We have described and demonstrated an extension of multi-speckle diffusing wave
spectroscopy adapted to characterize in a simple way the kinetics of micro-structure
dynamics during drying processes. This method allows one to follow the evolution of
a drying process in a very reactive way and with a high dynamic range. We call this
technique ASII for “Adaptive Speckle Imaging Interferometry”, a method based on
the efficient quantification of the speckle pattern evolution (via the inter-image
distance d2), its characterization through a single number (the speckle rate SR) and an
adaptive algorithm that continuously optimizes the acquisition and processing chain
with respect to the product dynamics. These new methods are implemented in a novel
commercial instrument, called HORUS®, specialized in the non-invasive analysis of
the film formation and drying processes analysis.